A sprinter explodes out of the starting block with an acceleration of +2.79 m/s2 , which she sustains for 1.65 s. Then her acceleration drops to zero for the rest of the race. What is her velocity at t = 1.65 s and at the end of the race?

3434m/s

585 To find the velocity of the sprinter at different times during the race, we can use the equations of motion.

First, let's calculate the velocity at t = 1.65 s. The initial velocity is assumed to be zero because the sprinter starts from rest.

We can use the formula:

v = u + at

where:
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
t is the time.

Plugging in the values:
u = 0 m/s (initial velocity)
a = 2.79 m/s^2 (acceleration)
t = 1.65 s (time)

v = 0 + (2.79)(1.65)
v = 4.60 m/s

Therefore, the velocity of the sprinter at t = 1.65 s is 4.60 m/s.

Next, let's find the velocity at the end of the race when the acceleration drops to zero. The sprinter will continue to move at a constant velocity.

To find the final velocity at the end of the race, we can use the 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 displacement.

Since the acceleration drops to zero, the equation simplifies to:

v = u

Plugging in the values:
u = 4.60 m/s (velocity at t = 1.65 s)

v = 4.60 m/s

Therefore, the velocity of the sprinter at the end of the race is also 4.60 m/s.