Question

A bus is moving at 10ms^-1 towards a traffic light.when the driver sees the light changes to red,the bus is ay a distance of 20m.the reaction tine of the driver us 0.5s and the deceleration is 4.5ms^-2.how far is the bus when it stops?

Answer 1

Answer on Question #43723 – Physics – Mechanics | Kinematics | Dynamics

A bus is moving at $10\mathrm{ms}\wedge -1$ towards a traffic light. When the driver sees the light changes to red, the bus is at a distance of $20\mathrm{m}$. The reaction time of the driver is 0.5s and the deceleration is $4.5\mathrm{ms}\wedge -2$. How far is the bus when it stops?

Solution:

$\mathrm{V}_0 = 10\frac{\mathrm{m}}{\mathrm{s}}$ – initial velocity of the bus;

$\mathrm{d}_0 = 20\mathrm{m}$ – distance to the traffic light;

$\mathrm{t}_0 = 0.5\mathrm{s}$ – reaction time of the driver;

$\mathrm{a} = 4.5\frac{\mathrm{m}}{\mathrm{s}^2}$ – deceleration of the bus;

$\mathrm{d}_1$ – distance from the bus to initial position;

$\Delta \mathrm{d}$ – distance to the traffic light when bus stops;

Rate equation for the bus:

$$0 = V _ {0} - a t$$ $$t = \frac {V _ {0}}{a}$$

Equation of motion for the bus:

$$\mathrm {d} _ {1} = \mathrm {V} _ {0} \mathrm {t} _ {0} + \mathrm {V} _ {0} \mathrm {t} - \frac {\mathrm {a t} ^ {2}}{2}$$

(1) in (2):

$$\mathrm {d} _ {1} = \mathrm {V} _ {0} \mathrm {t} _ {0} + \mathrm {V} _ {0} \mathrm {t} - \frac {\mathrm {a} \left(\frac {\mathrm {V} _ {0}}{\mathrm {a}}\right) ^ {2}}{2} = \mathrm {V} _ {0} \mathrm {t} _ {0} + \mathrm {V} _ {0} \cdot \frac {\mathrm {V} _ {0}}{\mathrm {a}} - \frac {\mathrm {V} _ {0} ^ {2}}{2 \mathrm {a} ^ {2}} = \mathrm {V} _ {0} \mathrm {t} _ {0} + \frac {\mathrm {V} _ {0} ^ {2}}{2 \mathrm {a}}$$ $$\Delta \mathrm {d} = \mathrm {d} _ {0} - \mathrm {d} _ {1} = \mathrm {d} _ {0} - \mathrm {V} _ {0} \mathrm {t} _ {0} - \frac {\mathrm {V} _ {0} ^ {2}}{2 \mathrm {a}} = 2 0 \mathrm {m} - 1 0 \frac {\mathrm {m}}{\mathrm {s}} \cdot 0. 5 \mathrm {s} - \frac {\left(1 0 \frac {\mathrm {m}}{\mathrm {s}}\right) ^ {2}}{2 \cdot 4 . 5 \frac {\mathrm {m}}{\mathrm {s} ^ {2}}} = 3. 9 \mathrm {m}$$

**Answer**: distance to the traffic light when bus stops will be $3.9\mathrm{m}$.

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