First slide

Instantaneous velocity

Question

A body has an initial velocity of 3 ms^-1 and has an acceleration of 1 ms^-1 normal to the direction of the initial velocity. Then its velocity 4 s after the start is

Easy

A

7 ms-¹ along the direction of initial velocity
B

7 ms-¹ along the normal to the direction of initial velocity.
C

7ms-¹ midway between the two directions
D

5 ms-¹ at an angle tan-1(4/3) with the direction of initial velocity.

Solution

$Let y_{x} = 3 {ms}^{- 1}, a_{x} = 0 yx = y_{x} + aytt = 0 + 1 \times 4 = 4 {ms}^{- 1} Angle made by the resultant velocity w . r . t . direction of initial velocity, i . e ., x - axis, is β = \tan^{- 1} \frac{V_{y}}{v_{x}} = \tan^{- 1} \frac{4}{3}$

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