The displacement - time graph of a particle at time t makes angle 45° with the time axis. After two seconds, it makes an angle 60° with the time axis. What is the average acceleration of the particle?

Question

The displacement - time graph of a particle at time t makes angle 45° with the time axis. After two seconds, it makes an angle 60° with the time axis. What is the average acceleration of the particle? (A) (1/2) (B) (√3/2) (C) ((√3-1)/2) (D) ((√3+1)/2)

Tardigrade Admin · Accepted Answer

Initial velocity, u= tan 45°=1 Velocity after 2 s , v= tan 60°=√3 ∴ Average acceleration, a av =(v-u/t)=(√3-1/2)

Q. The displacement - time graph of a particle at time $t$ makes angle $4 5^{\circ}$ with the time axis. After two seconds, it makes an angle $6 0^{\circ}$ with the time axis. What is the average acceleration of the particle?

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{( 3 - 1 )}{2}$

$\frac{( 3 + 1 )}{2}$

Initial velocity, $u = tan 4 5^{\circ} = 1$
Velocity after $2 s, v = tan 6 0^{\circ} = 3$
$∴$ Average acceleration, $a_{a v} = \frac{v - u}{t} = \frac{3 - 1}{2}$

Q. The displacement - time graph of a particle at time t makes angle 45∘ with the time axis. After two seconds, it makes an angle 60∘ with the time axis. What is the average acceleration of the particle?

21​

23​​

2(3​−1)​

2(3​+1)​