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?
Answer 1 of 2
To find the velocity of the sprinter at t = 1.65 s and at the end of the race, we need to use the kinematic equation that relates acceleration, initial velocity, time, and final velocity. The equation is:
v = u + at
Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
First, let's find the final velocity at t = 1.65 s. We know that the acceleration is +2.79 m/s^2, the initial velocity is 0 m/s (as the sprinter starts from rest), and the time is 1.65 s. Plugging these values into the equation, we have:
v1 = 0 + (2.79)(1.65)
v1 = 4.6035 m/s
Therefore, the velocity of the sprinter at t = 1.65 s is approximately 4.6035 m/s.
Next, let's find the final velocity at the end of the race. We know that the acceleration becomes zero, the initial velocity is v1 (the velocity at t = 1.65 s), and the time is the total race time minus 1.65 s. Let's assume the total race time is denoted as T. Plugging these values into the equation, we have:
v2 = 4.6035 + (0)(T - 1.65)
v2 = 4.6035 m/s
Therefore, the velocity of the sprinter at the end of the race is approximately 4.6035 m/s.
Note: It is worth mentioning that this calculation assumes the sprinter does not slow down or change acceleration after the initial acceleration phase. In a real race, other factors like air resistance and fatigue may also affect the sprinter's performance.