Question

an object travels back and forth along a straight line. its velocity, in centimeters per second, is given by the function $v(t)=13sin(\frac{pi}{45}t)$, where $t$ is time in seconds. what is the maximum velocity of the object? 0 cm/s 13 cm/s 26 cm/s 90 cm/s

Explanation:

Step1: Recall sine - function property

The range of the sine function $y = \sin(x)$ is $[- 1,1]$, i.e., $-1\leqslant\sin(x)\leqslant1$.

Step2: Analyze the given velocity function

The velocity function is $v(t)=13\sin(\frac{\pi}{45}t)$. Since $- 1\leqslant\sin(\frac{\pi}{45}t)\leqslant1$, when $\sin(\frac{\pi}{45}t) = 1$, the velocity $v(t)$ reaches its maximum value.

Step3: Calculate the maximum velocity

Substitute $\sin(\frac{\pi}{45}t)=1$ into $v(t)=13\sin(\frac{\pi}{45}t)$. We get $v(t)_{max}=13\times1 = 13$ cm/s.

Answer:

13 cm/s