Question

ques1.) Two forces (A - B) and (A + B) act at an angle 'e' such that the
magnitude of the resultant is V3A2+B2. Calculate the angle between the two forces.

(ques 2) A bike initially at rest, starts to move on a straight track and covers
a distance of 12,5 m in 10 seconds (assuming uniform acceleration).
Calculate acceleration of the bike.​

Answer 1

Answer:

Ques 1

the angle between them is 60 degree

Ques 2

the acceleration of the bike is 0.25 m/s/s

Explanation:

Ques 1)

As we know that if two vectors are at angle "theta" then the resultant of two vectors is given as

$R = \sqrt{P^2 + Q^2 + 2PQ cos\theta}$

so we will have

$P = A - B$

$Q = A + B$

$R = \sqrt{3A^2 + B^2}$

now we have

$3A^2 + B^2 = 2A^2 + 2B^2 + 2(A^2 - B^2) cos\theta$

$A^2 - B^2 = 2(A^2 - B^2) cos\theta$

$cos\theta = \frac{1}{2}$

$\theta = 60$

So the angle between them is 60 degree

Ques 2)

distance covered by the object while moving with uniform acceleration is given as

$d = v_i t + \frac{1}{2}at^2$

here we know that

$d = 12.5 m$

$t = 10 s$

$v_i = 0$

so we have

$12.5 = 0 + \frac{1}{2}a(10^2)$

$a = 0.25 m/s^2$

#Learn

Topic : Kinematics and vectors

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