Velocity and Displacement From Acceleration

Question

An object has a constant acceleration $$a(t)=4$$ ft/s² and an initial velocity $$v(0)=2$$ ft/s. The table shows the velocity $$v(t)$$ at selected times $$t$$. All of the following statements are true EXCEPT:

| $$t$$ (s) | $$v(t)$$ (ft/s) |
|---|---|
| 0 | 2 |
| 1 | 6 |
| 2 | 10 |
| 3 | 14 |

Accepted Answer

After integrating, the velocity function is $$v(t)=4*t+2$$, so the displacement after 3 seconds is simply computed as $$4*3+2$$.

Answer

The displacement is obtained by integrating the velocity function, i.e., $$s(t)=\int (4*t+2)\,dt$$.

Answer

The change in velocity over a time interval is given by $$v(b)-v(a)=\int_a^b 4\,dt$$.

Answer

Integrating the acceleration function yields $$v(t)=4*t+2$$, which correctly recovers the velocity function.

$t$ (s)	$v(t)$ (ft/s)
0	2
1	6
2	10
3	14

Velocity and Displacement From Acceleration

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