Question

An advertisement for the newest model of a Mercedes sports claims the car can go from 0 to 60miles per hour (mph) in just 3.3 seconds!a) How many meters per second (m/s) is 60 mph?b) In m/s^2(sometimes written as m/s/s also, just so you know), what is the supposed acceleration ofthe sports car?c) Impressed by this claim, Sherry buys one. She hops into her new Mercedes sports car and stepson the gas. She's an engineer and did the math later on; she discovered that her car's acceleration is6.7 m/s^2i) Is her car's acceleration faster or slower than the advertisement claims it should be? Do the math toprove and justify your answer.li) In seconds, how long did it actually take for Sherry's car to reach 60 mph (which ism/s, your answer to Part A)?

Answer 1

Part a)

One mile is approximately 1609 meters and one hour is 3600 seconds.

Then:

$\frac{60\text{ miles}}{1\text{ hour}}=\frac{60\times1609\text{ meters}}{3600\text{ seconds}}=26.81666...\frac{m}{s}$Part b)

Since the car goes from 0 to 26.82m/s in 3.3 seconds, then, the acceleration of the car is:

$a=\frac{\Delta v}{t}=\frac{26.82\frac{m}{s}}{3.3s}=8.13\frac{m}{s^2}$Part c)

i)

Since 6.7m/s^2 is less than 8.13m/s^2, then, the acceleration of her car is slower than the advertisement claims.

ii)

The time t that it takes to reach the speed v from rest with an acceleration a is:

$t=\frac{v}{a}$

Replace v=60mph, convert it to SI units and replace a=6.7m/s^2 to find the time that it takes to reach 60mph:

$t=\frac{60mph\times\frac{1609\frac{m}{mile}}{3600\frac{s}{h}}}{6.7\frac{m}{s^2}}=4.002s$

Therefore, the answers are:

Part a) 60mph is equal to 26.82 m/s.

Part b) The acceleration of the car as advertised is 8.13 m/s^2.

Part c1) Her car's acceleration is slower than the advertisement claims.

Part c2) It takes 4 seconds for her car to reach 60mph.