Question

The velocity of an object is given by the formula
v=2t^2+4t+2
Use intergration to calculate the distance travelled between t=4s and t=7s

Answer 1

Answer on Question #52849, Physics – Mechanics Kinematics | Dynamics

Question:

The velocity of an object is given by the formula

$$v = 2t^2 + 4t + 2$$

Use intergration to calculate the distance travelled between $t=4s$ and $t=7s$

Answer:

$$\begin{aligned} \int_{4}^{7} 2t^2 + 4t + 2\,dt &= \left. \frac{2t^3}{3} + 2t^2 + 2t \right|_{4}^{7} = \frac{2 \times 7^3}{3} + 2 \times 7^2 + 2 \times 7 - \left( \frac{2 \times 4^3}{3} + 2 \times 4^2 + 2 \times 4 \right) \\ &= \frac{686}{3} + 98 + 14 - \frac{128}{3} - 32 - 8 = 186 + 72 = 258 \end{aligned}$$

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