# Distance Time Graph

## Trending Questions

**Q.**A three-wheeler starts from rest, accelerates uniformly with 1 m s–2 on a straight road for 10 s, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second (n = 1, 2, 3….) versus n. What do you expect this plot to be during accelerated motion : a straight line or a parabola ?

**Q.**A woman starts from her home at 9.00 am, walks with a speed of 5 km h¯¹ on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 km h–1. Choose suitable scales and plot the x-t graph of her motion.

**Q.**The graph between the displacement x and time t for a particle moving in a straight line is shown in figure. During the interval OA, AB, BC and CD, the acceleration of the particle is

- OAABBCCD+0++
- OAABBCCD−0+0
- OAABBCCD+0−+
- OAABBCCD−0−0

**Q.**

Why is $\mathrm{displacement}=\mathrm{average}\mathrm{velocity}\mathrm{x}\mathrm{time}$, only when velocity is constant?

**Q.**

If a solid cylinder rolls up along a inclined plane with an initial velocity v. It will rise up to a height h equal to

**Q.**

Which of these is a correct distance-time graph for the motion of the body?

**Q.**The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. 3.19. Choose the correct entries in the brackets below ; (a) (A/B) lives closer to the school than (B/A) (b) (A/B) starts from the school earlier than (B/A) (c) (A/B) walks faster than (B/A) (d) A and B reach home at the (same/different) time (e) (A/B) overtakes (B/A) on the road (once/twice).

**Q.**The position of a particle moving along x-axis attime t is given by x = A sin ot where A and o arepositive constant. Select correct option.\lbrack Here a acceleration\rbrack(1) a wx(2) a 2x3(3) a ω 2A(4) a -2x

**Q.**

velocity is ω, angular acceleration is α and the torque is τ. Which of the following relations is correct?

**Q.**describe the concept of VELOCITY GRADIENT.with vidieo lecture

**Q.**Read the graph and comment on its nature.

- Velocity of the particle is negative.
- Velocity of the particle is positive.
- Initial position of the particle is zero.
- Particle is at rest throughout the time.

**Q.**The displacement time graph for two particles A and B are straight lines inclined at angles of 30∘ and 60∘ with the time axis. The ratio of velocities of VA:VB is

- 1:2
- 1:√3
- √3:1
- 1:3

**Q.**A partice is projected with velocity 10m/s at an angle 60^{0 }with the gound.Then the vertical component velocityvector when ins†an†an eous velocity becomes prependicular to intial velocity , i

**Q.**Will acceleration vector remain constant in ucm

**Q.**

The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 3.29:

Which of the following formulae are correct for describing the motion of the particle over the time-interval *t*_{2} to* t*_{1}?

(a) *x*(*t*_{2})* = x*(*t*_{1})* + v*(*t*_{1})(*t*_{2}*–t*_{1})* + *()*a*(*t*_{2}*–t*_{1})^{2}

(b) *v*(*t*_{2})*= v*(*t*_{1}) *+ a*(*t*_{2}*–t*_{1})

(c) *v*_{Average} *= *(*x*(*t*_{2}) *– x*(*t*_{1}))* /* (*t*_{2} *– t*_{1})

(d) *a*_{Average} *= *(*v*(*t*_{2})* – v*(*t*_{1}))* /* (*t*_{2} *– t*_{1})

(e) *x*(t_{2}) *= x*(t_{1})* + **v*_{Average}(t_{2} *– *t_{1})* + *()*a*_{Average}(t_{2} *– *t_{1})^{2}

(f) *x*(t_{2})* – x*(t_{1})* = *area under the *v–t *curve bounded by the *t*-axis and the dotted line shown.

**Q.**

In 10 seconds the angular speed of a bike increases from 1000rpm to 1800rpm. The angular acceleration of bike is

**Q.**The position-time graph of a particle of mass 2 kg moving along x-axis is shown in figure. The magnitude of impulse on particle at t=2 s is

- Zero
- 10 N s
- 20 N s
- 40 N s

**Q.**a particle in SHM has a velocity u v and accelerations a b in two of its positions find the dis†an ce between these two position

**Q.**6. If a body is slipping down an inclined plane with uniform velocity then what about angular acceleration is constant or 0 ?

**Q.**Figure 3.23 gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter14). Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s.