# Instantaneous acceleration

## Trending Questions

**Q.**A particle moves along a straight line. Its position at any instant is given by x=32t−8t33 where x is in m and t in s. The acceleration of the particle at the instant when particle is at rest will be

- −16 m/s2
- −32 m/s2
- 16 m/s2
- 32 m/s2

**Q.**A boy stretches a stone against the rubber tape of a catapult or 'gulel' (a device used to detach mangoes from the tree by boys in Indian villages) through a distance of 24 cm before leaving it. The tape returns to its initial normal position, accelerating the stone over the stretched length. The stone leaves the gulel with a speed of 2.2 m/s. Assuming that acceleration is constant while the stone was being pushed by the tape, find the magnitude.

- 8.1 m/s2
- 9.1 m/s2
- 10.1 m/s2
- 11.1 m/s2

**Q.**Given below are the equations of motion of four particles A, B, C and D.

xA=6t−3;

xB=4t2−2t+3;

xC=3t3−2t2+t−7;

xD=7cos60°−3sin30°

Which of these four particles move with uniform non-zero acceleration?

- A
- B
- C
- D

**Q.**

The relation between time and distance is t=αx2+βx where α and β are constants. The retardation is

2αv3

2βv3

2αβv3

2β2v3

**Q.**The acceleration of a particle is increasing linearly with time t as bt . The particle starts from the origin with an initial velocity vo . The distance travelled by the particle in time t will be

- v0t+13bt2
- v0t+13bt3
- v0t+16bt3
- v0t+12bt2

**Q.**Velocity (V) versus displacement (S) graph of a particle moving in a straight line is as shown in the figure. Given Vo=4 m/s and So=20 m.

Corresponding acceleration (a) versus displacement (S) graph of the particle would be

**Q.**A car accelerates uniformly from 13 ms–1 to 31 ms–1 while entering the motorway, covering a distance of 220 m. Then the acceleration of the car will be:

- 2.9 ms−2
- 1.8 ms−2
- 4 ms−2
- 2.2 ms−2

**Q.**The position of the particle is given by x=2t3−4t2+5 in m. The acceleration of the particle at 5 sec is

- 45 m/s2
- 48 m/s2
- 40 m/s2
- 52 m/s2

**Q.**Each of the four particles move along x axis. Their coordinate (in meters) as function of time (in seconds) are given by

**Particle 1:**x(t)=3.5−2.7t3

**Particle 2:**x(t)=3.5+2.7t3

**Particle 3:**x(t)=3.5+2.7t2

**Particle 4:**x(t)=3.5−3.4t−2.7t2

Which of these particles are speeding up for t>0?

- All four
- Only 1
- Only 2 and 3
- Only 2, 3 and 4

**Q.**A particle is moving along 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 average speed of the particle for the interval t=0 s to t=4 s is

- 1 m/s
- 0.5 m/s
- 2 m/s
- 1.5 m/s

**Q.**A particle moves along x-axis and its acceleration at any time t is a=2sin(πt), where t is in seconds and a is in m/s2. The initial velocity of particle (at time t=0) is u=0. The distance travelled (in meters) by the particle from time t=0 to t=1 s will be

- 2π
- 1π
- 4π
- None of these

**Q.**The velocity (V) versus displacement (S) graph of a particle moving in a straight line is as shown in the figure. Given Vo=4 m/s and So=20 m. At what displacement do velocity and acceleration have the same magnitudes?

- At S=5 m
- At S=10 m
- At S=30 m
- None of these

**Q.**Velocity (V) versus displacement (S) graph of a particle moving in a straight line is as shown in the figure. Given Vo=4 m/s and So=20 m.

Corresponding acceleration (a) versus displacement (S) graph of the particle would be

**Q.**A particle moves along X− axis. It's equation of motion is x=2t(t−2) where t is in seconds. Choose the correct statement(s).

- The particle moves with a non-uniform acceleration.
- The particle momentarily comes to rest at t=1 sec.
- The particle performs SHM
- The given equation represents uniformly accelerated motion for t>1 sec

**Q.**Velocity of a car as a function of time is given by v(t)=(4t3−et+sint) in m/s. The acceleration in ( m/s2) of the car as a function of time t is

- 12t2−et−cost
- t2−et+cost
- 12t2−et+cost
- t2+et+cost

**Q.**The displacement x of a particle depends on time t as x=αt2−βt3. Then,

- The particle will return to its starting point after time αβ
- The particle will come to rest after time 2α3β
- The initial velocity of the particle was zero but its initial acceleration was not zero
- No net force will act on the particle at t=α3β

**Q.**Motion described by two different objects are shown in the figure. The ratio of accleration of the objects i.e. aAaB is

- 3:2
- 5:3
- 2:3
- 3:5

**Q.**A Porsche undergoing uniformly accelerated motion can go from 0 km/h to 100 km/h in 10 s. What is its instantaneous acceleration?

- 2.77 m/s2
- 3.66 m/s2
- −3.66 m/s2
- 0 m/s2