The figure (Figure 1) shows the velocity of a solar-powered motorhome (RV) as a function of time. The driver accelerates from a stop sign, cruises for 20 s at a constant speed of 60 km/h, and then brakes to come to a stop 40 s after leaving the stop sign.

What is the instantaneous acceleration at t=35s??????****

It is given that, the driver accelerates from a stop sign, cruises for 20 s at a constant speed of 60 km/h, and then brakes to come to a stop 40 s after leaving the stop sign.

We know that acceleration is defined as the rate of change of velocity.

\(a=\dfrac{dv}{dt}\)

Where

dv is the change in velocity, dv = 0 - 60 m/s = -60 m/s

dt is the change in time, dt = 40 s - 30 s = 10 s

So, \(a=\dfrac{-60\ m/s}{10\ s}\)

\(a = -6\ m/s^2\)

From the graph it is clear that, from 30 s to 40 s the car is decelerating. So, at every second within this time the value of acceleration will be same i.e. \(-6\ m/s^2\).

onyebuchinnaji onyebuchinnaji · Answer 2 · 2021-11-05T17:35:11-04:00

The instantaneous acceleration of the car is 0.48 m/s².

The given parameters;

at time, t = 35 s
velocity of the car at the given time = 60 km/h

The velocity of the car in m/s, is calculated as follows;

\(v=60 \ \frac{km}{h} \times \frac{1 000 \ m}{1km} \times \frac{ 1 \ h}{3600 \ s} \\\\v = 16.67 \ m/s\)

The instantaneous acceleration of the car at t = 35s, is calculated as follows;

\(a = \frac{v}{t} \\\\a = \frac{16.67}{35} \\\\a = 0.48 \ m/s^2\)

Thus, the instantaneous acceleration of the car is 0.48 m/s².

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