Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
The figure shows the x-t plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t > 0? If not, suggest a suitable physical context for this graph.
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 man has to go 50 m due north, 40 m due east and 20 m due south to reach a field. (a) What distance he has to walk to reach the field? (b) What is his displacement from his house to the field?
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.
Refer to the graphs in figure. Match the following.
| Graph | Characteristic |
(a)  |
(i) has v > 0 and a < 0 throughout. |
(b)  |
(ii) has x > 0 throughout and has a point with v = 0 and a point with a = 0. |
(c)  |
(iii) has a point with zero displacement for t > 0. |
(d)  |
(iv) has v < 0 and a > 0. |
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.
Ship A is sailing towards the northeast with velocity `vecv = 30hati + 50hatj` km/hr where `hati` points east and `hatj`, north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing west at 10 km/hr. A will be at the minimum distance from B in ______.
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)
A car covers the first half of the distance between two places at 40 km/h and other half at 60 km/h. The average speed of the car is ______.
