Question

A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/ h and 40 km/h respectively. The velocity of the car midway between P and Q is

• A. $33.3\, km/h$
• B. $ 20\sqrt 2\, km/h$
• C. $ 25\sqrt 2\, km/h$
• D. $35\, km/h$

Answer 1

The Correct Option is D

To find the velocity of the car midway between points P and Q, we need to understand the concept of motion under uniform acceleration.

The car has velocities of 30 km/h and 40 km/h at points P and Q respectively. Under uniform acceleration, the velocity of a car midway between two points on a straight path is the average of these velocities because uniform acceleration implies constant change in velocity. Mathematically, the average velocity v_{\text{average}} is calculated as:

v_{\text{average}} = \frac{v_1 + v_2}{2}

Given:

• Velocity at P, v_1 = 30\, km/h
• Velocity at Q, v_2 = 40\, km/h

Now substitute these values into the formula:

v_{\text{average}} = \frac{30 + 40}{2} = \frac{70}{2} = 35\, km/h

Thus, the correct answer is that the velocity of the car midway between P and Q is 35\, km/h.

This can also be intuitively understood: since the car accelerates uniformly, its speed in the midpoint is simply the arithmetic mean of the starting and ending speeds over that interval.