Question

A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q seperated by a distance with velocity 30 km/hr and 40 km/hr respectively. The velocity of the car midway between P and Q is a) 33.3 km/hr b) 20$\sqrt{2}$ km/hr c) 25$\sqrt{2}$km/hr d) 35 km/hr.

Answer 1

Option (a) is correct.

Step 1: Given

Velocity at P=30 km/hr(u=initial velocity)

Velocity at Q=40 km/hr(v=final velocity)

Let the distance between P and Q is s.

Assume acceleration of the car is a.

Step 2: Formula used

v²=u²+2*a*s (3rd equation of motion)

Step 3: Finding velocity at midway between P and Q

40²=30²+2*a*s

2as=1600-900

as=$\frac{700}{2}$

as=350

Now,

the distance of midway between P and Q is $\frac{s}{2}$.

so, distance=$\frac{s}{2}$

u=30km/hr

v₁= velocity at midway between P and Q

using, (v₁²=u²+2as)

v₁²=30²+$\frac{2as}{2}$

v₁²=900+350

v₁²=1150

v₁=35.35 km/hr

Hence, the velocity of the car midway between P and Q is 35.35 km/hr.