Question

A typical male sprinter can maintain his maximum acceleration for 2.0 s, and his maximum speed is 10 m> s. After he reaches this maximum speed, his acceleration becomes zero, and then he runs at constant speed. Assume that his acceleration is constant during the first 2.0 s of the race, that he starts from rest, and that he runs in a straight line.

How far has the sprinter run when he reaches his maximum speed?

Answer 1

The sprinter, starting from rest and accelerating at a constant rate for 2 seconds to a maximum speed of 10 m/s, covers a distance of 10 meters by the time he reaches his maximum speed.

Step-by-step explanation:

To calculate how far the sprinter has run when he reaches his maximum speed, we can use the kinematic equations for uniformly accelerated motion. The sprinter accelerates from rest with a constantly maintained acceleration until reaching his maximum speed. We can use the following equation to find the distance:

s = ut + 0.5at^2

Where:

• s is the distance (what we are trying to find).
• u is the initial velocity (0 m/s, as he starts from rest).
• t is the time (2.0 s as given in the question).
• a is the acceleration (which we will calculate).

First, we need to find the acceleration using the formula v = u + at, where:

• v is the final velocity (10 m/s).
• u is the initial velocity (0 m/s).
• t is the time (2.0 s).

Rearranging the formula to calculate acceleration, we get:

a = (v - u) / t

a = (10 m/s) / 2.0 s = 5 m/s^2

Now that we have the acceleration, we can find the distance:

s = 0 m/s * 2.0 s + 0.5 * 5 m/s^2 * (2.0 s)^2

s = 0 + 0.5 * 5 m/s^2 * 4 s^2

s = 10 m

Thus, the sprinter has run 10 meters when he reaches his maximum speed.