Question

A sprinter explodes out of the starting block with an acceleration of +4.2 m/s2, which she sustains for 0.9 s. Then, her acceleration drops to zero for the rest of the race. (a) What is her velocity at t = 0.9 s. m/s (b) What is her velocity at the end of the race? m/s

Answer 1

The velocity at t = 0.9 s is 3.78 m/s. The velocity at the end of the race is also 3.78 m/s.

Step-by-step explanation:

(a) To find the velocity at t = 0.9 s, we need to calculate the distance traveled during that time period. Using the equation: v = u + at. The initial velocity (u) is 0 m/s since the sprinter starts from rest. The acceleration (a) is +4.2 m/s². And the time (t) is 0.9 s. Plugging these values into the equation, we get: v = 0 + (4.2)(0.9) = 3.78 m/s. Therefore, the sprinter's velocity at t = 0.9 s is 3.78 m/s.

(b) To find the velocity at the end of the race, we need to calculate the distance traveled after t = 0.9 s. Since the acceleration drops to zero, the sprinter will continue at a constant velocity for the rest of the race. To find this final velocity, we can use the equation: vf = vi + at, where vf is the final velocity, vi is the initial velocity at t = 0.9 s, a is the acceleration, and t is the time after t = 0.9 s. Since the acceleration is zero, the equation simplifies to: vf = vi. Therefore, the sprinter's velocity at the end of the race is 3.78 m/s.

Answer 2

a) 3.78 m/s

b) 3.78 m/s

Step-by-step explanation:

a )From the equations of kinematics we know that

Vf - Vi = at

since Initial speed Vi = 0

acceleration = 4.2 m/s2

so we have

Vf = a t

= (4.2) (0.9)

= 3.78 m/s

velocity at t = 0.9 s. m/s is 3.78 m/s

b) If the sprinter maintains constant velocity then acceleration becomes zero.

So velocity is 3.78 m/s