Question

How much force is needed to accelerate a $ 1kg $ toy car at a rate of $ 2m{s^{ - 2}} $ ?

Answer 1

Hint: To solve this problem use Newton’s Second law of motion. Newton’s Second law of motion states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. Put the values of mass and acceleration to find the required force.
Newton’s second law can be written as, $ \vec a = \dfrac{{\vec F}}{m} $ where, $ \vec a $ is the acceleration of the object, $ \vec F $ is the net force applied on the object and $ m $ is the mass of the object.

Complete step by step answer:
We have given here a toy car of mass $ m = 1kg $ which is needed to accelerate with a rate of $ \vec a = 2m{s^{ - 2}} $ .
Now, from Newton’s Second law of motion states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. Mathematically it can be written as, $ \vec a = \dfrac{{\vec F}}{m} $ where, $ \vec a $ is the acceleration of the object, $ \vec F $ is the net force applied on the object and $ m $ is the mass of the object.
Also we can write the equation as, $ \vec F = m\vec a $
Now we have mass $ m = 1kg $ which is needed to accelerate with a rate of $ \vec a = 2m{s^{ - 2}} $ .
So putting the values we get,
  $ \left| {\vec F} \right| = 1 \times 2 = 2N $ , the direction of the force is in the horizontal direction or parallel to the direction of acceleration.
Hence, $ 2N $ force must be applied to the toy car horizontally to accelerate it at a rate of $ 2m{s^{ - 2}} $ .

Note:
The direction of force applied is always important. If we apply the same amount of force at an angle the car will not accelerate with the same rate rather it will accelerate with a lesser rate than $ 2m{s^{ - 2}} $ . But, if the horizontal component of that force is $ 2N $ then the toy car will always accelerate with the rate of $ 2m{s^{ - 2}} $ no matter in which angle the force is applied.