# Introduction to acceleration

## Trending Questions

**Q.**

The relation between time $t$ and distance $x$ is $t=\alpha {x}^{2}+\beta x$ where $\alpha $ and $\beta $ are constants. The retardation is

$-2\alpha {v}^{3}$

$2\beta {v}^{3}$

$2\alpha \beta {v}^{3}$

$2\beta 2{v}^{3}$

**Q.**The acceleration-displacement graph of a partice moving in a straight line is shown in the figure. Initial velocity of the particle is zero. Find the velocity of the particle when displacement of the particle is 12 m.

- 3√2 m/s
- 2√5 m/s
- 4 m/s
- 4√3 m/s

**Q.**A man loses 20% of his velocity after running through 108 m. If the rate by which he is losing his velocity remains constant, what is the maximum distance he will cover?

- 218 m
- 300 m
- 324 m
- 192 m

**Q.**The displacement (s) of a particle is proportional to the first power of time t, i.e., s∝t; then the acceleration of the particle is

- Infinite
- Zero
- A small finite value
- A large finite value

**Q.**What is the acceleration, if the body starts from the rest and travels a distance of s m in 2 seconds?

- 23s m/s2
- 32s m/s2
- 13s m/s2
- 12s m/s2

**Q.**

What do you mean by positive acceleration?

**Q.**A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further will it penetrate before coming to rest assuming that it faces constant resistance to motion?

- 1.5 cm
- 1.0 cm
- 3.0 cm
- 2.0 cm

**Q.**The x coordinates of a particle at any time t are given by x=7t+4t2 where x is in m and t in s. The acceleration of the particle at 5 s is

- zero
- 8 m/s2
- 20 m/s2
- 40 m/s2

**Q.**What is the acceleration, if the body starts from the rest and travels a distance of s m in 2 seconds?

- 23s m/s2
- 32s m/s2
- 13s m/s2
- 12s m/s2

**Q.**An object moves velocity →v having constant accelaration →a. Which of the following expressions are variable quantities ?

- d|→v|dt
- ∣∣ ∣∣d→vdt∣∣ ∣∣
- d(|→v|2)dt
- d⎛⎜⎝→v−→|v|⎞⎟⎠dt

**Q.**A car starting from rest accelerates at the rate f through a distance s, then continues at constant speed for time t and then decelerates at rate f2 to come to rest. If the total distance covered is 15s, then which one is correct?

- s=ft272
- s=ft24
- s=ft26
- s=ft22

**Q.**If velocity of the particle is given by v=√x, where x denotes the position of the particle and initially particle was at x=4, then which of the following are correct ?

- At t=2 s, the position of the particle is x=9
- Particle's acceleration at t=2 sec, is 1 m/s2
- Particle's acceleration is 12 m/s2 throughout the motion
- Particle will never go in negative direction from its starting position

**Q.**A body starts from orgin and moves along x-axis such that its velocity is v=(4t3−2t) m/s. Acceleration of particle when it is 2 m from origin is.

- 10 m/s2
- 20 m/s2
- 11 m/s2
- 22 m/s2

**Q.**A sports car can accelerate uniformly to a speed of 162 km/h in 5 s. Its maximum braking retardation is 6 m/s2. The minimum time in which it can travel 1 km, starting from rest and ending at rest, in seconds is?

**Q.**On seeing a speed limit road sign, you apply brakes that bring your car from the speed of 30 m/s to a speed of 20 m/s, covering a distance of 100 m at a constant deceleration. How much time is required for the given decrease in speed?

- 3 s
- 4 s
- 2 s
- 5 s

**Q.**The velocity of a body is dependent on its position as v=√x, where v and x are in SI units. Then its acceleration

- increases linearly
- decreases linearly
- remains constant
- first increases and then decreases

**Q.**A particle is moving along the positive x-axis and at t=0, the particle is at x=0. The acceleration of the particle is a function of time. The acceleration at any time t is given by a=2(1–[t]) where [t] is the greatest integer function. Assuming that the particle is at rest initially, the displacement of the particle in 4 s is

- 1 m
- 2 m
- 6 m
- 4 m

**Q.**A body starts from rest with acceleration 2 m/s2 till it attains the maximum velocity, then retards to rest with 3 m/s2. If total time taken is 10 seconds then maximum speed attained is

- 12 m/s
- 8 m/s
- 6 m/s
- 4 m/s

**Q.**A car which has an initial velocity of 4 m/s accelerates at the rate of 2 m/s2 for 5 s. What will be the distance (in m) that it covers in these 5 s ?

**Q.**A car which has an initial velocity of 4 m/s accelerates at the rate of 2 m/s2 for 5 s. What will be the distance (in m) that it covers in these 5 s ?

**Q.**The displacement (s) of a particle is proportional to the first power of time t, i.e., s∝t; then the acceleration of the particle is

- Infinite
- Zero
- A small finite value
- A large finite value

**Q.**A particle returns to the starting point after 10 s. if the rate of change of velocity during the motion is constant, then its location after 7 s will be same as that after

- 3 s
- 4 s
- 5 s
- 6 s

**Q.**A car moving with a speed of 50 km/h can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is:

- 12 m
- 18 m
- 24 m
- 6 m

**Q.**Motion of two objects are shown in the figure, which object has greater acceleration?

- A
- B
- Both have equal acceleration
- Can't say

**Q.**The acceleration of a particle starting from rest varies with time according to the relation a=kt+c. The velocity v of the particle after time t will be

- kt2+ct
- 12(kt2+ct)
- 12(kt2+4ct)
- kt22+ct

**Q.**On seeing a speed limit road sign, you apply brakes that bring your car from the speed of 30 m/s to a speed of 20 m/s, covering a distance of 100 m at a constant deceleration. How much time is required for the given decrease in speed?

- 3 s
- 4 s
- 2 s
- 5 s

**Q.**A parachutist drops first freely from an aeroplane for 10 s and then parachute opens out. Now he descends with a net retardation of 2.5 m/s2. If he bails out of the plane at a height of 2495 m and g=10 m/s2, his velocity on reaching the ground in m/s will be

**Q.**Choose the correct option:

i. Accelerated motion means acceleration and velocity have same direction.

ii. It is possible that particle have zero acceleration with non-zero velocity.

iii. When acceleration of the particle is positive, it is under accelerated motion.

- Statement (i), (ii) and (iii) are true.
- Statement (i) and (ii) are true.
- Statement (ii) and (iii) are true.
- Statement (i) and (iii) are true.

**Q.**If a particle moves with a constant velocity,

- Its acceleration is positive
- Its acceleration is negative
- Its acceleration is zero
- Its speed is zero

**Q.**A car starts from rest and accelerates at 5 m/s2. At t=4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6 s?

(g=10 m/s2)

- 20√2 m/s, 10 m/s2
- 20 m/s, 5 m/s2
- 20 m/s, 0 m/s2
- 20√2 m/s, 0 m/s2