Question

If a driver is going 81.7 km/hr hits the brakes giving the truck a deceeration of 4.19 while it travels 23.1 m how i find velocity of the truck in m/s at the end of this displacement and how much time has elapsed. Can someone tell me what my variables would be like what number goes where for vi vf d a and t and what formula i would use no answers please

Answer 1

First convert km/h to m/s:
\[\frac{ 81.7 }{ 3.6 } = 22.694_{m/s}\]
If you were given displacement, use the displacement formula:
\[y _{f}=y_i+v _{i} \times t + \frac{ a \times t^2 }{ 2 }\]

Answer 2

\[23.1 = 0 + 22.694\times t + \frac{ -4.19 \times t^2 }{ 2 }\]

Answer 3

\[46.2=45.928t-4.19t^2\]
\[4.19t^2-45.928+46.2=0\]
solve quadratic equation:
\[t_1=9.840_{\sec}\]
\[t_2=1.120_{\sec}\]

Answer 4

Pick the time that is relevant to what was asked, because both are correct.
I would assume the driver just brakes, and doesn't start reversing back, so I'm going to use the shorter time.
In the velocity formula:
\[v_f=v_i+a \times t\]
\[v_f=22.694+(-4.19)\times1.120\]
\[v_f = 18_{m/s}\]

Answer 5

Thank You so much