A car is travelling at 23.4m/s to the right when the driver puts on the brakes. The car has an acceleration of -4.50m/s^2 while the brakes are acting.
(a) How long does it take to bring the car to a stop?
(b) Calculate the displacement of the car.
v = Vi + a t
0 = 23.4 - 4.50 t
t = 23.4/4.50
x = average speed * t
= (23.4/2) t
To solve these questions, we can use the equations of motion from Newtonian physics.
(a) To find the time it takes for the car to come to a stop, we can use the equation:
v = u + at
where:
v = final velocity (0 m/s, since the car comes to a stop)
u = initial velocity (23.4 m/s to the right)
a = acceleration (-4.50 m/s^2, since the brakes are acting)
t = time
Rearranging the equation to solve for time, we have:
t = (v - u) / a
Plugging in the given values, we get:
t = (0 - 23.4) / -4.50
Calculating this expression, we find:
t ≈ 5.20 seconds
So, it takes approximately 5.2 seconds for the car to come to a stop.
(b) To calculate the displacement of the car, we can use the equation:
s = ut + (1/2)at^2
where:
s = displacement
u = initial velocity (23.4 m/s to the right)
t = time (5.2 seconds)
a = acceleration (-4.50 m/s^2)
Plugging in the given values, we have:
s = (23.4 × 5.2) + (1/2)(-4.50)(5.2)^2
Calculating this expression, we find:
s ≈ 60.6 meters
So, the displacement of the car is approximately 60.6 meters to the right.