Question

An automobile whose speed is increasing at a rate of 0.6 m/s2 travels along a circular road with a radius of 20m. When instantaneous acceleration is 4m/s?

Answer 1

To solve this problem, we can use the relationship between acceleration, velocity, and radius in circular motion:

a = v^2 / r

where: a is the centripetal acceleration, v is the instantaneous velocity, and r is the radius of the circular road.

Given: Acceleration (a) = 4 m/s^2 Radius (r) = 20 m

We need to find the instantaneous velocity (v) at this point.

Rearranging the formula, we have:

v = √(a * r)

Substituting the values:

v = √(4 m/s^2 * 20 m) v = √(80 m^2/s^2) v ≈ 8.94 m/s

Therefore, the instantaneous velocity of the automobile at that point is approximately 8.94 m/s.