The displacement 'x' of a particle moving along a straight line at time t is given by
x = 29+at+azt. The acceleration of the particle is :-
(1) a
(2) a
(3) 2a,
(4) 3az
1
Answers
Answer :
- Acceleration of the particle, a = 0 m/s²
Explanation :
Given :
- Displacement of the particle, x = 29 + at + azt
To find :
- Acceleration of the particle, a = ?
Knowledge required :
- Differentiating the displacement of a particle with respect to time, gives the velocity of that particle.
Formula for velocity of a particle :
⠀⠀⠀⠀⠀⠀⠀⠀⠀v = dx/dt⠀
[Where, v = Velocity of the particle, x = displacement of the particle]
- Differentiating the velocity of a particle with respect to time, gives the acceleration of that particle.
Formula for acceleration of a particle :
⠀⠀⠀⠀⠀⠀⠀⠀⠀a = dv/dt⠀
[Where, a = acceleration of the particle, v = velocity of the particle.
Solution :
To find the velocity of the particle :
⠀By using the formula for Velocity of a particle and substituting the values in it, we get :
⠀⠀=> v = dx/dt = d(29 + at + azt)/dt
⠀⠀=> v = d(29)/dt + d(at)/dt + d(azt)/dt
⠀⠀=> v = 0 + a + az
⠀⠀=> v = a + az
⠀⠀⠀⠀∴ v = (a + az) m/s
Now,
To find the acceleration of the particle :
⠀By using the formula for acceleration of a particle and substituting the values in it, we get :
⠀⠀=> a = dv/dt = d(a + az)/dt
⠀⠀=> a = d(a)/dt + d(az)/dt
⠀⠀=> a = 0 + 0
⠀⠀=> a = 0
⠀⠀⠀⠀∴ a = 0 m/s²
Hence, the acceleration of the particle is 0 m/s².