Question

Determine the energy required to accelerate a 1270-kg car from 10 to 60 km/h on an uphill road with a vertical rise of 40 m. (Round the final answer to the nearest whole number.) The energy required to accelerate the car uphill is kJ.

Answer 1

The energy required to accelerate the car uphill is approximately 1910680 J.

Step-by-step explanation:

To determine the energy required to accelerate a car uphill, we need to calculate the change in kinetic energy and the gravitational potential energy.

First, let's find the change in kinetic energy:

Initial speed = 10 km/h = 2.78 m/s

Final speed = 60 km/h = 16.67 m/s

Change in kinetic energy = (1/2) * mass * (final speed)^2 - (1/2) * mass * (initial speed)^2

= (1/2) * 1270 kg * (16.67 m/s)^2 - (1/2) * 1270 kg * (2.78 m/s)^2

= 1412280.45 J

Next, let's find the gravitational potential energy:

Vertical rise = 40 m

Gravitational potential energy = mass * gravitational acceleration * vertical rise

= 1270 kg * 9.8 m/s^2 * 40 m

= 498400 J

Finally, the energy required to accelerate the car uphill is the sum of the change in kinetic energy and the gravitational potential energy:

Total energy required = Change in kinetic energy + Gravitational potential energy

= 1412280.45 J + 498400 J

= 1910680.45 J

Rounding to the nearest whole number, the energy required to accelerate the car uphill is approximately 1910680 J.

Answer 2

E= 679.83 KJ

Step-by-step explanation:

Given that

m = 1270 kg

u = 10 km/h

We know that 1 km/h = 0.27 m/s

u = 2.7 m/s

v= 16.67 m/s

h = 40 m

By using energy conservation

The energy required =E

`E=(1)/(2)m (v^2-u^2)+mgh`

Now by putting the values in the above equation

`E=(1)/(2)* 1270* (16.67^2-2.7^2)+1270* 10* 40`

We are taking g= 10 m/s²

Now by solving above equation we get

E= 679830.30 J

E= 679.83 KJ

The energy required will be 679.83 KJ