Question

A driver of a car travelling at 52 km per hour apply the brakes and accelerates uniformly in the opposite direction the car stops in 5 seconds another driver going at 3 km per hour in another car applies is break slowly and stops in 10 seconds on the same graph paper plot the speed versus time graph for the two cars which of the two cars travel father after the brakes are applied.

Answer 1

Hint- To solve this question, we use the basic theory related to the topic speed, distance and time. In this question, for the first car: Initial velocity Final velocity, Time taken, for second car: Initial velocity, Final velocity, Time taken, the distance travelled by a moving body is given by the area under its speed-time graph.
To convert km/hr. to m/s we need to multiply by $\dfrac{{\text{5}}}{{{\text{18}}}}$.

Complete step-by-step answer:

Now, As given in question-
Initial speed of the car A: u=52 km/hr.
                                                    = 52${\times }\dfrac{{\text{5}}}{{{\text{18}}}}$= 14.44 m/s
The car stops in 5 seconds i.e v=0 at t=5

Initial speed of the car B: u=3km/hr.
                                                     = 3${\times }\dfrac{{\text{5}}}{{{\text{18}}}}$= 0.83 m/s
With the help of these initial and final points for both the cases, we can plot the graph of speed vs time.
Area under the speed-time graph gives the distance covered.
∴ Distance covered by car A (\[{{\text{x}}_{\text{A}}}\]) = $\dfrac{1}{2} \times 14.44 \times 5$= 36.1 m
∴ Distance covered by car A (\[{{\text{x}}_{\text{B}}}\]) = $\dfrac{1}{2} \times 0.83 \times 10$=4.15 m
Thus, car A travels more distance than B.

Note- In this question, the data given in the problem are in different units. So, we should first convert the km unit into m units. And with the help of these initial and final points for both the cases, we can plot the graph of speed vs time.