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The engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph). At full power, the car can accelerate from zero to 32.0 mph in time 1.20 s.At full power, how long would it take for the car to accelerate from 0 to 64.0mph ?

Answer :

Answer:

[tex]t=5.3687\ s[/tex]  is the time taken by the car to accelerate the desired range of the speed from zero at full power.

Explanation:

Given:

Range of speed during which constant power is supplied to the wheels by the car is [tex]0\ mph\ to\ 70\ mph[/tex].

  • Initial velocity of the car, [tex]v_i=0\ mph[/tex]
  • final velocity of the car during the test, [tex]v_f=32\ mph=14.3052\ m.s^{-1}[/tex]
  • Time taken to accelerate form zero to 32 mph at full power, [tex]t=1.2\ s[/tex]
  • initial velocity of the car, [tex]u_i=0\ mph[/tex]
  • final desired velocity of the car, [tex]u_f=64\ mph=28.6105\ m.s^{-1}[/tex]

Now the acceleration of the car:

[tex]a=\frac{v_f-v_i}{t}[/tex]

[tex]a=\frac{14.3052-0}{1.2}[/tex]

[tex]a=11.921\ m.s^{-1}[/tex]

Now using the equation of motion:

[tex]u_f=u_i+a.t[/tex]

[tex]64=0+11.921\times t[/tex]

[tex]t=5.3687\ s[/tex] is the time taken by the car to accelerate the desired range of the speed from zero at full power.

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