7. A car has a mass of 1000 kg and is travelling
at 20 m/s.
The brakes then exert a steady force of 5000 N.
a) What is the deceleration?
b) How long does it take to stop the car?
a) To find the deceleration, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
Given:
Mass (m) = 1000 kg
Force (F) = 5000 N
Using the formula: F = ma
5000 = 1000 * a
Divide both sides by 1000:
a = 5000 / 1000
a = 5 m/s²
Therefore, the deceleration of the car is 5 m/s².
b) To find the time it takes to stop the car, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given:
Initial velocity (u) = 20 m/s
Final velocity (v) = 0 m/s
Acceleration (a) = -5 m/s² (negative because it is deceleration)
Using the formula: v = u + at
0 = 20 + (-5)t
Rearrange the equation:
5t = 20
Divide both sides by 5:
t = 20 / 5
t = 4 seconds
Therefore, it takes 4 seconds to stop the car.
a) To find the deceleration, we can use Newton's second law, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration (F = m*a).
Given:
Mass of the car (m) = 1000 kg
Force applied by the brakes (F) = 5000 N
Using the equation F = m*a, we can rearrange it to find the acceleration (a).
a = F/m
a = 5000 N / 1000 kg
a = 5 m/s²
Therefore, the deceleration of the car is 5 m/s².
b) To find the time it takes to stop the car, we can use the kinematic equation:
v = u + at
Where:
v = final velocity (0 m/s)
u = initial velocity (20 m/s)
a = deceleration (-5 m/s²)
Rearranging the equation to solve for time (t):
t = (v - u) / a
t = (0 - 20) / -5
t = 4 seconds
Therefore, it takes 4 seconds to stop the car.