Question

An object moves in a circle of radius 21 m with its speed given by v = 3.6 1.5t², with v in meters per second and t in seconds. What is the speed of the object at t = 3.5 s?

Answer 1

The speed of the object at t = 3.5 s, calculated using the given velocity-time equation, is 21.375 m/s.

Step-by-step explanation:

To calculate the speed of the object at t = 3.5 s when it is moving in a circle of radius 21 m, we substitute t = 3.5 s into the provided equation for velocity: v(t) = 3.0 + 1.5t2 m/s. After substituting, we get v(3.5 s) = 3.0 + 1.5(3.5)2 m/s.

First, calculate the t2 term: (3.5)2 = 12.25. Then, multiply by 1.5: 1.5 × 12.25 = 18.375. Finally, add 3.0 to it: 3.0 + 18.375 = 21.375 m/s. Therefore, the speed of the object at t = 3.5 s is 21.375 m/s.