Question

A particle travels in a straight line with a constant acceleration of 3 meters per second per second. If the velocity of the particle is 10 meters per second at time 2 seconds, how far does the particle travel during the time interval when its velocity increases from 4 meters per second to 10 meters per second?

Answer 1

We can use the kinematic equation:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.

At time t=2 seconds, the velocity of the particle is 10 m/s. We can use this information to find the initial velocity:

v = u + at

10 = u + 3(2)

u = 4 m/s

Now we can use the same equation to find the distance traveled when the velocity increases from 4 m/s to 10 m/s:

v^2 = u^2 + 2as

(10)^2 = (4)^2 + 2(3)s

100 = 16 + 6s

84 = 6s

s = 14 meters

Therefore, the particle travels a distance of 14 meters during the time interval when its velocity increases from 4 meters per second to 10 meters per second