Question

Area under a velocity time graph is distance travelled. Find, from the following formula x=t^3 + t^2 - 2t + 4
The distance travelled when an object moves through a toroidal magnet for x ms
x ms in this case = 0.4

Answer 1

Answer on Question #58155-Engineering-Mechanical Engineering

Area under a velocity time graph is distance travelled. Find, from the following formula $x = t^3 + t^2 - 2t + 4$

The distance travelled when an object moves through a toroidal magnet for $x$ ms

$x$ ms in this case = 0.4

Solution

The distance travelled when an object moves through a toroidal magnet is

$$\begin{array}{l} d = \int_{0}^{4} x(t) \, dt = \int_{0}^{4} (t^3 + t^2 - 2t + 4) \, dt = \left(\frac{t^4}{4} + \frac{t^3}{3} - t^2 + 4t\right)_{0}^{4} = \left(\frac{4^4}{4} + \frac{4^3}{3} - 4^2 + 4 \cdot 4\right) - (0) \\ = \frac{256}{3} \, m \approx 85.3 \, m. \end{array}$$

Answer: $\frac{256}{3} \, m \approx 85.3 \, m$.

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