SATHEE: Motion in a Straight Line

Motion in a Straight Line - Result Question 32

33. 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 $30 k m / h$ and $40 k m / h$ respectively. The velocity of the car midway between $P$ and $Q$ is

[1988]

(a) $33.3 k m / h$

(b) $20 \sqrt{2} k m / h$

(d) $35 k m / h$

Topic 3: Relative Velocity

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Answer:

Correct Answer: 33. (c)

Solution:

$u = 30 k m / h$

$v = 40 k m / h$

$a = \frac{40^{2} - 30^{2}}{2 x} = \frac{350}{x} [∵ v^{2} = u^{2} + 2 a s]$

Also, velocity at mid point is given by $v_{m}$ ,

$\Rightarrow v_{m} = u^{2} + 20 (7)$

$\Rightarrow v_{m}^{2} - 30^{2} = 2 \times \frac{350}{x} \times \frac{x}{2}$

This gives $v = 25 \sqrt{2} k m / h$

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Motion in a Straight Line - Result Question 32

33. 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 30km/h and 40km/h respectively. The velocity of the car midway between P and Q is

Topic 3: Relative Velocity

Answer:

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33. 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 $30 k m / h$ and $40 k m / h$ respectively. The velocity of the car midway between $P$ and $Q$ is