Advertisements
Advertisements
प्रश्न
The velocity-displacement graph of a particle is shown in figure.
- Write the relation between v and x.
- Obtain the relation between acceleration and displacement and plot it.
उत्तर
a. Consider the point P(x, v) at any time t on the graph such that angle ABO is θ such that tan θ = `(AQ)/(QP) = ((v_0 -v))/x = v_0/x_0`
When the velocity decreases from v0 to zero during the displacement, the acceleration becomes negative.
`v_0 - v = (v_0/x_0)x`
`v = v_0(1 - x/x_0)`
Is the relation between v and x.
b. `a = (dv)/(dt) = ((dv)/(dt))((dx)/(dx)) = ((dv)/(dx)) ((dx)/(dt))`
`a = (- v_0)/(x_0) v`
`a = ((v_0^2)/(x_0^2))x - (v_0^2/x_0)`
At `x = 0`
`a = (-v_0^2)/x_0`
At `a = 0`
`x = x_0`
The points are `(0, (-v_0^2)/x_0)` and `B(x_0, 0)`
APPEARS IN
संबंधित प्रश्न
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 the figure. Choose the correct entries in the brackets below;
- (A/B) lives closer to the school than (B/A)
- (A/B) starts from the school earlier than (B/A)
- (A/B) walks faster than (B/A)
- A and B reach home at the (same/different) time
- (A/B) overtakes (B/A) on the road (once/twice).
A police van moving on a highway with a speed of 30 km h–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h–1. If the muzzle speed of the bullet is 150 m s–1, with what speed does the bullet hit the thief’s car? (Note: Obtain that speed which is relevant for damaging the thief’s car).
Suggest a suitable physical situation for the following graphs:
A particle moves along the X-axis as x = u (t − 2 s) + a (t − 2 s)2.
(a) the initial velocity of the particle is u
(b) the acceleration of the particle is a
(c) the acceleration of the particle is 2a
(d) at t = 2 s particle is at the origin.
A particle starts from the origin, goes along the X-axis to the point (20 m, 0) and then return along the same line to the point (−20 m, 0). Find the distance and displacement of the particle during the trip.
In the following figure Shows the graph of velocity versus time for a particle going along the X-axis. Find the acceleration
In the following figure Shows the graph of velocity versus time for a particle going along the X-axis. Find the distance travelled in 0 to 10s
In the following figure Shows the graph of velocity versus time for a particle going along the X-axis. Find the displacement in 0 to 10 s.
A ball is dropped and its displacement vs time graph is as shown figure (displacement x is from ground and all quantities are +ve upwards).
- Plot qualitatively velocity vs time graph.
- Plot qualitatively acceleration vs time graph.
A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be: (Given cos135° = - 0.7)
