A Sprinter's Acceleration Calculation in a 100-m Race
A sprinter in a 100-m race accelerates uniformly for the first 71 m and then runs with constant velocity.
Answer: The acceleration of the sprinter is 1.4 m/s² Explanation: Hi there! The equation of position of the sprinter is the following: x = x0 + v0 · t + 1/2 · a · t² Where: x = position of the sprinter at a time t. x0 = initial position. v0 = initial velocity. t = time. a = acceleration. Since the origin of the frame of reference is located at the starting point and the sprinter starts from rest, then, x0 and v0 are equal to zero: x = 1/2 · a · t² At t = 9.9 s, x = 71 m 71 m = 1/2 · a · (9.9 s)² 2 · 71 m / (9.9 s)² = a a = 1.4 m/s² The acceleration of the sprinter is 1.4 m/s² Final answer: The sprinter's acceleration can be calculated by solving two equations from physics: the first formula of motion (final velocity equals initial velocity plus acceleration times time) and the formula for final velocity (distance divided by time). The result is an approximate acceleration of 0.72 m/s². Explanation: The question requires the use of kinematics, a topic in physics. The formula to calculate uniform acceleration is given by a = 2*(final velocity - initial velocity) / time. Here, final velocity is the velocity achieved after 71m, initial velocity is 0 (standing start), and time is 9.9s. However, we are not given the final velocity. We will have to use the first formula of motion, v = u + at, in which v is the final velocity, u is the initial velocity, a is acceleration, and t is time. Simultaneously, we have v = d/t where d is distance and t is time. Solving these two equations will give the acceleration (a). From the first formula of motion and the equation v = d/t, it's clear the sprinter's final velocity (when he/she stops accelerating) is 71m/9.9s which equals approximately 7.17 m/s. Substituting into the first formula of motion gives 7.17 m/s = 0 + a*9.9s, which simplifies to a = 7.17 m/s / 9.9s. This gives us an acceleration of approximately 0.72 m/s².