Astopwatch starts while race car travels at 4 m/s from the pit area and accelerates at a uniform rate to a speed of 23 m/s in 2 s moving on a circular track of radius 527 m. assuming constant tangential acceleration, find (a) the tangential acceleration, and (b) the radial acceleration, at the instant when the speed is v = 16 once you have both of those find the magnitude of a at any moment

(a) Tangential acceleration:

The tangential acceleration is given by:

where

v = 23 m/s is the final velocity of the car

u = 4 m/s is the initial velocity of the car

t = 2 s is the time taken for the car to accelerate from u to v

Substituting the numbers into the formula, we find

(b) Radial acceleration:

The radial acceleration is equivalent to the centripetal acceleration, which is given by:

where

v = 16 m/s is the tangential speed

r = 527 m is the radius of the circular orbit

Substituting numbers, we find