Question

An object accelerates from a stop at 5m/s^2 to the east. After 10 seconds it reaches its maximum velocity. After another 75 seconds it turns back toward the starting point. It immediately slows down and moves at 15m/s until it reaches the start point where it stops. What is the avg velocity of the object?

Answer 1

The average velocity of the object was -492.5 m/s (to the west).

Step-by-step explanation:

The average velocity of an object can be calculated by dividing the total displacement by the total time taken. In this case, the object starts at rest and accelerates to 15 m/s in 10 seconds. The displacement during this time can be calculated using the formula S = ut + 1/2at^2, where u is the initial velocity, t is the time, and a is the acceleration. The displacement is 0.5 * 5 * 10^2 = 250 m. After reaching its maximum velocity, the object turns back and slows down to a velocity of 0 m/s in 75 seconds. The displacement during this time can be calculated using the same formula, but with u as the final velocity and a as the deceleration. The displacement is 0.5 * (-15) * 75^2 = -42187.5 m.

Adding the two displacements, we get a total displacement of 250 m - 42187.5 m = -41937.5 m.

The total time taken is 10 s + 75 s = 85 s.

Therefore, the average velocity is the total displacement divided by the total time: -41937.5 m / 85 s = -492.5 m/s (to the west).