Question

Draw schematically the velocity time graph of a particle accelerating at 2 m/s2



starting from rest up to a time of 5 sec. Indicate in the graph the velocity at the end of 5 sec . Find from the graph the displacement suffered by the particle in 5 sec. ​

Answer 1

Explanation:

Draw schematically the velocity time graph of a particle accelerating at 2 m/s2

starting from rest up to a time of 5 sec. Indicate in the graph the velocity at the end of 5 sec . Find from the graph the displacement suffered by the particle in 5 sec.

Answer 2

Given:

The initial velocity of the particle, u = 0, since it starts from rest.

The acceleration of the particle, a = 2 m/s².

The time of acceleration of the particle, t = 5 s.

To Find:

Using the given details, we have to draw the velocity-time graph of the particle and find out the displacement suffered by the particle in 5 seconds.

Solution:

Using the first equation of motion, we can find out the velocity of the given particle as follows.

$v = u + at.$

Substituting the given values, we get,

$v = o+2t = 2t.$

Using the above equation, when t (in s) = 0, 1, 2, 3, 4, and 5, we get the values of v as v (in m/s) = 0, 2, 4, 6, 8 ,and 10, respectively.

A velocity-time graph is then drawn as follows, with velocity on the Y-axis and time on the X-axis.

The displacement suffered by the particle in 5 s is found using the second equation of motion.

$Displacement, S = ut + \frac{1}{2}at^2.$

Substituting the given values, the above equation becomes,

$S = 0.t + \frac{1}{2}.2.t^2 = t^2.$

When t = 5, the displacement is,

$S = t^2 = (5)^2 = 25 m.$

Hence, the velocity-time graph is plotted, and the displacement suffered by the particle in 5 seconds is 25m.

#SPJ2