A little help please?

Question

A little help please?

Spotting a police car, you brake your Porsche from a speed of 100 km/h
to a speed of 80.0 km/h during a displacement of 88.0 m, at a constant acceleration.

a. What is that acceleration?
b. How much time is required for the given decrease in speed?

1 Answer

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Answer 1 · 2018-07-02T19:24:55

a. $a = - 1.579 \frac{m}{s^{2}}$ $a = -1.579 m/s^2$
b. $t = 3.52 s$ $t = 3.52 s$

Explanation:

We have velocity in km/hr and displacement in m. Since we have to make a unit conversion, might as well do it so it will yield the answer in the normal (SI) units for acceleration.

$100 \frac{k m}{h r} \cdot \frac{1000 m}{1 k m} \cdot \frac{1 h r}{3600 s} = 27.78 \frac{m}{s}$ $100 (km)/(hr) * (1000 m)/(1 km)*(1 hr)/(3600 s) = 27.78 m/s$

$80.0 \frac{k m}{h r} \cdot \frac{1000 m}{1 k m} \cdot \frac{1 h r}{3600 s} = 22.22 \frac{m}{s}$ $80.0 (km)/(hr) * (1000 m)/(1 km)*(1 hr)/(3600 s) = 22.22 m/s$

a. Using the formula of motion $v^{2} = u^{2} + 2 \cdot a \cdot d$ $v^2 = u^2 + 2*a*d$

#(22.22 m/s)^2 = (27.78 m/s)^2 + 2a88.0 m

$493.7 \frac{m^{2}}{s^{2}} = 771.7 \frac{m^{2}}{s^{2}} + 176 m \cdot a$ $493.7 m^2/s^2 = 771.7 m^2/s^2 + 176 m*a$

$a = \frac{493.7 \frac{m^{2}}{s^{2}} - 771.7 \frac{m^{2}}{s^{2}}}{176 m} = - 1.579 \frac{m}{s^{2}}$ $a = (493.7 m^2/s^2 - 771.7 m^2/s^2)/(176 m) = -1.579 m/s^2$

b. Since the acceleration was constant, we can use the average velocity, and the distance to determine the time.

$t = \frac{88.0 m}{\frac{1}{2} \cdot (27.78 \frac{m}{s} + 22.22 \frac{m}{s})} = 3.52 s$ $t = (88.0 m)/(1/2*(27.78 m/s + 22.22 m/s)) = 3.52 s$

As a double-check, if we convert $v = u + a \cdot t$ $v = u + a*t$ to $t = \frac{v - u}{a}$ $t = (v - u)/a$ and plug in the data, let's see if we get the same time.

$t = \frac{22.22 \frac{m}{s} - 27.78 \frac{m}{s^{2}}}{- 1.579 \frac{m}{s^{2}}} = 3.52 s$ $t = (22.22 m/s - 27.78 m/s^2)/(-1.579 m/s^2) = 3.52 s$

I hope this helps,
Steve

Science

Math

Humanities

... and beyond

A little help please?

Spotting a police car, you brake your Porsche from a speed of 100 km/h
to a speed of 80.0 km/h during a displacement of 88.0 m, at a constant acceleration.

a. What is that acceleration?
b. How much time is required for the given decrease in speed?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A little help please?

Spotting a police car, you brake your Porsche from a speed of 100 km/h to a speed of 80.0 km/h during a displacement of 88.0 m, at a constant acceleration. a. What is that acceleration? b. How much time is required for the given decrease in speed?

1 Answer

Explanation:

Related questions

Impact of this question

Spotting a police car, you brake your Porsche from a speed of 100 km/h
to a speed of 80.0 km/h during a displacement of 88.0 m, at a constant acceleration.

a. What is that acceleration?
b. How much time is required for the given decrease in speed?