Question

Car starts from a stop sign and moves along a straight road so its position as a function of time is presented by the following formula x(t) = αt2 –β t3, where α =2.4 m/s^2, β = 0.38 m/s^3.

a. Calculate the average velocity of the car from t = 0 to t = 5 s.
b. Calculate the instantaneous velocity of the car at t = 0, t = 5 s, t = 10 s.
c. Calculate the time it takes for the car to be again at rest.
d. How far from the starting point will the car be at rest?

Answer 1

a. To calculate the average velocity of the car from t = 0 to t = 5 s, we need to find the displacement of the car during that time interval. We can do this by subtracting the initial position from the final position. Plugging in the values into the formula, x(5) - x(0), we get (2.4 * 5^2 - 0.38 * 5^3) - (2.4 * 0^2 - 0.38 * 0^3). Simplifying the equation gives us the average velocity.

b. To calculate the instantaneous velocity of the car at specific times, we can find the derivative of the position function with respect to time, which gives us the velocity function. Plugging in the values of t into the velocity function will give us the instantaneous velocity at those times.

c. To find the time it takes for the car to be at rest, we need to find the time when the velocity of the car is zero. We can set the velocity function equal to zero and solve for t.

d. To find how far the car is from the starting point when it is at rest, we can plug in the time value we found in part c into the position function and calculate the displacement.