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## Homework Statement

a vehicle of mass 200kg accelerates from rest up to 40km/h in 15seconds up an incline of 1 in 8. The resistance to motion can be considered to be in two parts, the first being due to friction and constant at 50 N/tonne with the second part being due to air resistance and being equal to 0.02v2 + v Newtons, where v is in km/hr.

a) Calculate the resistance to motion at 40km/h

b) Calculate the effort required to achieve 40km/h

c) Calculate the power required

d) we are later asked as part of coursework to choose a electric motor size for vehicle

## Homework Equations

## The Attempt at a Solution

**a)**whilst travelling at constant velocity

Force of air resistance (N) = 0.02*40^2+40 =

**72 N**

Rolling resistance (N) = 50 * 0.2t =

**10 N**

Force of incline (N) = 200*9.81*1/8 =

**245.25**

total resistance to motion at 40km/h (N) = 72+10+245.25 (N) =

**327.25 N**

**b)**Effort required = total resistance to motion + ma

to find a

v = 40km/h = 11.1m/s

u = 0 m/s

t = 15 s

a = ? m/s^2

v = u + at

11.1 (m/s)= a (m/s^2)*15(s)

a = 0.74 m/s^2

effort required = E = 327.25 (N)+ (200(kg)*0.74(m/s^2))

E =

**475.25 N**

**c)**

to find work done we need distance travelled

s = ut + 0.5at^2

s = 0.5*0.74(m/s^2)*15^2(t)

s = 83.25 m

workdone = 475.25(N)*83.25(m) = 39564.6 joules

Power = workdone/time = 39865.6(j)/15(s) = 2637.6 j/s (watts)

Power (hp) = 2598.2 / 745.7 = 3.49 hp

the answer I obtained doesn't take into account the varing air resistance would i need to find an average and recalculate?

in terms of selecting a suitable size motor if i work out the power needed at 39.9km/h with a acceleration of 0.74m/s^2 the power needed is

power = (total resistance + ma)*v

power = (475.25(N)+0.74(m/s^2)*200(kg))*11.1(m/s)

power = 6918 j/s

power (hp) = 6918/754.7 = 9.28 hp

I'm a little confused as why the power required to reach 40km/h is so less than power needed at 39.9km/h with a acceleration 0.74m/s^s. have i done calc wrong? what size motor do i go for? please help.