from equqtion t equal to x+3 .find velocity and acceleration t equal 1second here x is distance
To find the velocity and acceleration at t = 1 second, we need to differentiate the equation t = x + 3 with respect to time.
1. Differentiating x + 3 with respect to t will give us the velocity function v(t):
dv/dt = dx/dt
Since t = x + 3, we can rewrite this as:
dv/dt = d(x + 3)/dt
dv/dt = dx/dt
The derivative of a constant (in this case, 3) with respect to time is zero, so:
dv/dt = dx/dt = 0
Therefore, the velocity v(t) is 0.
2. To find the acceleration, we need to differentiate the velocity function v(t) with respect to t:
da/dt = dv/dt = 0
The derivative of a constant (in this case, 0) with respect to time is also zero, so:
da/dt = dv/dt = 0
Therefore, the acceleration a(t) is also 0.
In summary:
- At t = 1 second, the velocity is 0 m/s.
- At t = 1 second, the acceleration is 0 m/s².