A car of mass 1000kg travels with a velocity 45km/h on a rough road and it is brought to a rest after 10s. What is the force exerted on the car?
Vo = 45000/3600s = 12.5 m/s.
V = Vo + a*t = 0,
12.5 + a*10 = 0,
a = -1.25 m/s^2.
F = M*a =
The force opposes the motion; therefore, the force will be negative.
To calculate the force exerted on the car, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a).
Given:
Mass of the car (m) = 1000 kg
Initial velocity (v) = 45 km/h
Time taken (t) = 10 s
First, we need to convert the velocity from km/h to m/s, as the unit of acceleration is in meters per second squared (m/s²).
1 km = 1000 m
1 hour = 3600 seconds
Converting the velocity:
45 km/h = (45 * 1000) m / (1 * 3600) s
= 125 / 4 m/s
= 31.25 m/s (approx.)
Now, we need to calculate the acceleration (a) using the formula:
a = (change in velocity) / t
Change in velocity = final velocity - initial velocity
Change in velocity = 0 m/s - 31.25 m/s
= -31.25 m/s (since the car comes to rest)
Acceleration:
a = (change in velocity) / t
= (-31.25 m/s) / (10 s)
= -3.125 m/s² (negative sign indicates deceleration)
Finally, we can calculate the force exerted on the car using Newton's second law:
F = m * a
= 1000 kg * (-3.125 m/s²)
= -3125 N
Therefore, the force exerted on the car is -3125 N (negative sign indicates that the force is acting in the opposite direction of motion, causing deceleration or braking).