An object moving with constant acceleration at time t=0 its speed is v. , at t=t. its speed is v./2 , at t=2t. its speed is v./4 . What will be its speed at time t=3t.?
To find the speed of the object at time t=3t, we need to determine the acceleration and use it to calculate the speed.
Let's break down the problem step by step:
1. Given:
- Speed at t=0: v
- Speed at t=t: v/2
- Speed at t=2t: v/4
2. We can begin by calculating the acceleration (a) of the object using the given information:
To calculate acceleration, we'll use the formula: a = (v2 - v1) / (t2 - t1)
- Speed at t=0: v (v1)
- Speed at t=t: v/2 (v2)
- Time at t=0: 0 (t1)
- Time at t=t: t (t2)
Plugging in these values, we have:
a = (v/2 - v) / (t - 0)
= (v/2 - 2v/2) / t
= (-v/2) / t
= -v / (2t)
Therefore, the acceleration (a) is -v / (2t).
3. Now that we have the acceleration, we can determine the speed at time t=3t.
To find the speed, we'll use the formula: v = u + at
- Initial speed (u) at t=0: v
- Acceleration (a): -v / (2t)
- Time (t): 3t
Plugging in these values, we get:
v = v + (-v / (2t)) * 3t
= v - (3v / 2)
= v/2
Therefore, the speed of the object at time t=3t is v/2.
So, the object will have a speed of v/2 at time t=3t.