Question

Statement (1): A truck and a car moving with equal kinetic energy are stopped by equal retarding force. Both will cover equal distance to stop.
Statement (2): A car moving towards east suddenly changes its direction towards north with same speed. Its acceleration is zero.
In the light of given statements, choose the most appropriate answer from the options given below.

• A. Both (1) and (2) are true
• B. Both (1) and (2) are false
• C. (1) is true, (2) is false
• D. (1) is false, (2) is true

Answer 1

The Correct Option is C

The given problem involves analyzing two statements related to physics concepts. Let's evaluate each statement individually to determine their validity.

1. Statement 1: A truck and a car moving with equal kinetic energy are stopped by equal retarding force. Both will cover equal distance to stop.
   • The kinetic energy (KE) of an object is given by KE = \frac{1}{2} m v^2, where m is the mass and v is the velocity of the object.
   • When both the truck and the car have equal kinetic energy and are stopped by the same retarding force, the equation of motion used is v^2 = u^2 + 2a s, where v is the final velocity (0 in this case), u is the initial velocity, a is acceleration (retarding force per unit mass, thus negative), and s is the stopping distance.
   • Rearranging: 0 = u^2 - 2a s \Rightarrow s = \frac{u^2}{2a}.
   • Since both the truck and the car have equal kinetic energy, and both use the same retarding force, they'll have equal stopping distances according to the kinetic energy equivalency and motion equations. Thus, Statement 1 is true.
2. Statement 2: A car moving towards the east suddenly changes its direction towards the north with the same speed. Its acceleration is zero.
   • Changing the direction of an object implies a change in velocity, even if the speed remains constant. Velocity is a vector quantity, hence has both magnitude and direction.
   • Acceleration is defined as the rate of change of velocity. Since there is a change in the direction of velocity from east to north, the car experiences an acceleration (centripetal), even though the speed remains constant.
   • Thus, Statement 2 is false because a change in velocity's direction entails a non-zero acceleration.

Based on the analysis above:

• Statement 1 is true.
• Statement 2 is false.

The correct option is: (1) is true, (2) is false.