A cart starts from rest and accelerates uniformly at 4.0 m/s² for 5.0 s.It next maintains the velocity it has reached for 10 s.Then it slows down at a steady rate of 2.0 m/s² for 4.0 s.What is the final speed of the car? A)20 m/s B)16 m/s C)12 m/s D)10 m/s

Question

Quizplus · Accepted Answer

Using the equations of motion:

For the first phase (acceleration):
v = u + at
where u = 0, a = 4.0 m/s^2 and t = 5.0 s
v = 0 + 4.0 * 5.0 = 20 m/s

For the second phase (constant velocity):
v = u + at
where a = 0 and t = 10 s
v = 20 m/s (unchanged)

For the third phase (deceleration):
v^2 = u^2 + 2as
where u = 20 m/s, a = -2.0 m/s^2 and s = (20 m/s) * (10 s) + (1/2) * (-2.0 m/s^2) * (4.0 s)^2 = 180 m
v^2 = (20 m/s)^2 + 2(-2.0 m/s^2)(180 m) = 244 m^2/s^2
v = sqrt(244) = 12 m/s

Therefore, the final speed of the cart is 12 m/s, thus the correct choice is C.

A Cart Starts from Rest and Accelerates Uniformly at 4