Question

A car is traveling on a level highway at a speed of 15m/s. A braking force of 3000 N brings the car to a stop in 10 seconds. The mass of the car is?
A) 1500kg
B) 2000kg
C) 2500kg
D) 3000kg
E) 45,000kg

Answer 1

Answer on Question #45039 - Physics - Mechanics | Kinematics | Dynamics

A car is traveling on a level highway at a speed of $15\mathrm{m / s}$ . A braking force of 3000 N brings the car to a stop in 10 seconds. The mass of the car is?

A) $1500\mathrm{kg}$

B) $2000\mathrm{kg}$

C) $2500\mathrm{kg}$

D) $3000\mathrm{kg}$

E) 45,000kg

Solution.

$F_{b}$ - a braking force;

$v_{0}$ - an initial speed of the car;

$a$ - a deceleration of the car;

$m - a$ mass of the car;

$mg - a$ weight of the car;

$t - a$ time to the stop;

$N - a$ normal force of the car;

From the equation for the velocity:

$$\vec {v} = \overrightarrow {v _ {0}} + \vec {a} t;$$

$\vec{v} = 0$, because car stopped.

$$0 = \overrightarrow {v _ {0}} + \vec {a} t;$$

Projection on OX:

$$0 = v _ {0 x} - a _ {x} t;$$ $$v _ {0 x} = a _ {x} t;$$ $$v _ {0 x} = v _ {0}; a _ {x} = a;$$ $$v _ {0} = a t; (1)$$

Newton's second law in vector form:

$$m \vec {a} = \overrightarrow {F _ {b}} + \vec {N} + m \vec {g};$$

Projection on OX:

$$- m a _ {x} = - F _ {b x} + 0 + 0 = - F _ {b x};$$

$N = 0$ and $mg = 0$ - projections on OX are zero.

$$m a _ {x} = F _ {b x};$$ $$a _ {x} = \frac {F _ {b x}}{m};$$ $$F _ {b x} = F _ {b}; a _ {x} = a;$$ $$a = \frac {F _ {b}}{m}; (2)$$

From equations (1) and (2) we have:

$$v _ {0} = \frac {F _ {b}}{m} t;$$ $$m = \frac {F _ {b}}{v _ {0}} t;$$ $$m = \frac {3 0 0 0 N}{1 5 \frac {m}{s}} \cdot 1 0 s = 2 0 0 0 k g.$$

Answer: B) 2000kg.

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