Question

A stopwatch starts while race car travels at 7 m/s from the pit area and accelerates at a uniform rate to a speed of 30 m/s in 19 s moving on a circular track of radius 511 m.

Assuming constant tangential acceleration, find
(a) the tangential acceleration, and
(b) the radial acceleration,at the instant when the speed is v = 15
Once you have both of those ... find the magnitude of a at any moment

Answer 1

The tangential acceleration of the race car is 1.21 m/s², and the radial acceleration at a velocity of 15 m/s is approximately 0.44 m/s². Using these values, the magnitude of total acceleration of the car can be calculated as approximately 1.30 m/s².

Step-by-step explanation:

To find the tangential acceleration (at), we use the formula at = (v - u) / t, where v is the final velocity, u is the initial velocity, and t is the time taken to reach that velocity. For the given problem, the car starts at 7 m/s and accelerates to 30 m/s in 19 seconds. Plugging in these values gives us a tangential acceleration of (30 m/s - 7 m/s) / 19 s = 23/19 m/s2 = 1.21 m/s2.

When the car's velocity is v = 15 m/s, we can calculate the radial acceleration (ar) with the formula ar = v2 / r, where r is the radius of the circular track. Plugging in the values gives us a radial acceleration of (15 m/s)2 / 511 m = 225/511 m/s2 ≈ 0.44 m/s2.

To find the total acceleration (a) at any moment, we use the formula a = √(at2 + ar2). With the earlier found accelerations, we substitute at = 1.21 m/s2 and ar ≈ 0.44 m/s2 to calculate the magnitude of total acceleration. Thus, a ≈ √(1.212 + 0.442) m/s2 ≈ 1.30 m/s2.