Question

A frictionless toy car is placed on a ramp, which is inclined at an unknown angle with respect to the horizontal. Starting from rest, the car is allowed to roll freely down the ramp. After a time interval of Δ=0.67 s, the car has traveled a distance of =1.2 m down the ramp and is moving with speed f. Find the speed of the car at the end of the 0.67 s time interval.

Answer 1

The final speed of the toy car at the end of the given time period is 3.58 m/s.

The given parameters;

• distance traveled by the car, s = 1.2 m
• time of motion of the car, t = 0.67 s
• initial velocity of the car, u = 0

The acceleration of the car is calculated as;

$s = ut + \frac{1}{2} at^2\\\\1.2 = 0 + 0.5\times a\times (0.67)^2\\\\1.2 = 0.225a\\\\a = \frac{1.2}{0.225} \\\\a = 5.33 \ m/s^2$

The final velocity of the toy car is calculated as;

$v_f^2 = u^2 + 2as\\\\v_f^2 = 0 + 2\times 5.33 \times 1.2\\\\v_f^2 = 12.792\\\\v_f = \sqrt{12.792} \\\\v_f = 3.58 \ m/s$

Thus, the final speed of the toy car at the end of the given time period is 3.58 m/s.

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