Question

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t)=bt²−ct³, where b = 2.70 m/s² and c = 0.130 m/s³ .Calculate the average velocity of the car for the time interval t= 0 to t= 10.0 s. vav = m/s

Answer 1

The average velocity of the car over the time interval from t = 0 to t = 10.0 s is calculated to be 14 m/s using the position-time equation given.

Step-by-step explanation:

The question asks for the calculation of the average velocity of a car over a given time interval, using a specific position-time equation. The provided equation is x(t) = bt² - ct³, with b = 2.70 m/s² and c = 0.130 m/s³. To find the average velocity, we need the initial and final positions (x(0) and x(10.0 s)) and the time interval, Δt (10.0 s).

• Calculate the initial position x(0) = (2.70 m/s²)(0²) - (0.130 m/s³)(0³) = 0 m.
• Calculate the final position x(10.0 s) = (2.70 m/s²)(10.0 s)² - (0.130 m/s³)(10.0 s)³ = 270 m - 130 m = 140 m.
• Since Δt = 10.0 s, the average velocity (Šav) is the change in position (Δx) over the change in time (Δt): Šav = Δx / Δt = (140 m - 0 m) / 10.0 s = 14 m/s.

Therefore, the average velocity of the car over the time interval from t = 0 to t = 10.0 s is 14 m/s.

Answer 2

The average velocity of the car over the time interval from t = 0 to t = 10.0 s is calculated to be 14 m/s using the position-time equation given.

Step-by-step explanation:

The question asks for the calculation of the average velocity of a car over a given time interval, using a specific position-time equation. The provided equation is x(t) = bt² - ct³, with b = 2.70 m/s² and c = 0.130 m/s³. To find the average velocity, we need the initial and final positions (x(0) and x(10.0 s)) and the time interval, Δt (10.0 s).

Calculate the initial position x(0) = (2.70 m/s²)(0²) - (0.130 m/s³)(0³) = 0 m.

Calculate the final position x(10.0 s) = (2.70 m/s²)(10.0 s)² - (0.130 m/s³)(10.0 s)³ = 270 m - 130 m = 140 m.

Since Δt = 10.0 s, the average velocity (Šav) is the change in position (Δx) over the change in time (Δt): Šav = Δx / Δt = (140 m - 0 m) / 10.0 s = 14 m/s.

Therefore, the average velocity of the car over the time interval from t = 0 to t = 10.0 s is 14 m/s.