Question

Un coche que circula a 90km/h necesita adelantar a un camión que circula a la misma velocidad para lo que precisa alcanzar 120km/h en 3 segundos. Si su coche posee una aceleración de 1,6m/s a dicha velocidad ¿lo consigue? ¿cuanto tiempo le ha costado en realidad?

Answer 1

Answer: he needs to accelerate for 5.2 seconds to reach the speed of 130km/h

Step-by-step explanation:

This can be translated to:

A car running at 90 km/h needs to overtake a truck driving at the same speed, for which it needs to reach 120 km/h in 3 seconds. If your car has an acceleration of 1.6 m/s^2 at that speed. Does the driver reach the speed? How long has it actually cost to reach that velocity?

The acceleration is 1.6m/s^2

To obtain the velocity, we can integrate over time and get:

v(t) = (1.6m/s^2)*t + v0

where v0 is the initiall velocity, 90km/h.

v(t) = (1.6m/s^2)*t + 90km/h

after 3 seconds, the velocit of the car is:

v(3) = (1.6m/s^2)*3s + 90km/h = 4.8 m/s + 90km/h

So we need to change the units in the first therm.

1km = 1000m

1h = 3600s

4.8m/s = 4.8m/s*(1km/1000m)*(3600s/1h) = 4.8(3600/1000) km/h

4.8 m/s = 17.28 km/h

Then the velocity after accelerating for 3 seconds is:

v(3s) = 90km/h + 17.28km/h = 107.28km/h

So he does not reach the wanted speed.

Then we can find the time needed to reach the speed as:

(1.6m/s^2)*t + 90km/h = 120km/h

(1.6m/s^2)*t = 30km/h

lets tranfor the right term to m/s

30km/h = 30*(1000/3600) m/s = 8.3m/s

then our equation is:

(1.6m/s^2)*t = 8.3m/s

t = 8.3m/s/ (1.6m/s^2) = 5.2 s

So he needs 5.2 seconds to reach the needed speed.