A car has mass m. A person needs to push the car with force F in order to give the car acceleration a.

Question 9

A car has mass m. A person needs to push the car with force F in order to give the car

acceleration a. The person needs to push the car with force 2F in order to give the car

acceleration 3a.

Which expression gives the constant resistive force opposing the motion of the car?

A ma               B 2ma             C 3ma             D 4ma

Reference: Past Exam Paper – November 2016 Paper 11 & 13 Q11

Solution:

Answer: A.

Let the resistive force be R.

When the person applies a force F, there is a resultant acceleration a on the car. Remember that there is a resistive force R (in the opposite direction to F).

Resultant force = mass × acceleration

F – R = ma                  ------------------- (1)

The person needs to apply a force of 2F to produce a resultant acceleration of 3a.

Resultant force = mass × acceleration

2F – R = m × 3a

2F – R = 3ma              ------------------- (2)

From equation (1), F = ma + R. Replace F by (ma + R) in equation (2).

2(ma + R) – R = 3ma

2ma + 2R – R = 3ma

R = 3ma – 2ma

 
Resistive force R = ma