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fredd [130]
2 years ago
7

A car accelerates from rest with an acceleration of 5 m/s^2. The acceleration decreases linearly with time to zero in 15 s, afte

r which the car continues with constant speed. At what time t will the car have moved 500 m from its starting point?
Engineering
1 answer:
Tpy6a [65]2 years ago
3 0

Answer: At time 18.33 seconds it will have moved 500 meters.

Explanation:

Since the acceleration of the car is a linear function of time it can be written as a function of time as

a(t)=5(1-\frac{t}{15})

a=\frac{d^{2}x}{dt^{2}}\\\\\therefore \frac{d^{2}x}{dt^{2}}=5(1-\frac{t}{15})

Integrating both sides we get

\int \frac{d^{2}x}{dt^{2}}dt=\int 5(1-\frac{t}{15})dt\\\\\frac{dx}{dt}=v=5t-\frac{5t^{2}}{30}+c

Now since car starts from rest thus at time t = 0 ; v=0 thus c=0

again integrating with respect to time we get

\int \frac{dx}{dt}dt=\int (5t-\frac{5t^{2}}{30})dt\\\\x(t)=\frac{5t^{2}}{2}-\frac{5t^{3}}{90}+D

Now let us assume that car starts from origin thus D=0

thus in the first 15 seconds it covers a distance of

x(15)=2.5\times 15^{2}-\farc{15^{3}}{18}=375m

Thus the remaining 125 meters will be covered with a constant speed of

v(15)=5\times 15-\frac{15^{2}}{6}=37.5m/s

in time equalling t_{2}=\frac{125}{37.5}=3.33seconds

Thus the total time it requires equals 15+3.33 seconds

t=18.33 seconds

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A police officer in a patrol car parked in a 70 km/h speed zone observes a passing automobile traveling at a slow, constant spee
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Answer:

S = 0.5 km

velocity of motorist = 42.857 km/h

Explanation:

given data

speed  = 70 km/h

accelerates uniformly = 90 km/h

time = 8 s

overtakes motorist =  42 s

solution

we know  initial velocity u1 of police = 0

final velocity u2 = 90 km/h = 25 mps

we apply here equation of motion

u2 = u1 + at  

so acceleration a will be

a = \frac{25-0}{8}

a = 3.125  m/s²

so

distance will be

S1 = 0.5 × a × t²

S1 = 100 m = 0.1 km

and

S2 = u2 ×  t

S2 = 25  × 16

S2 = 400 m = 0.4 km  

so total distance travel by police

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S = 0.5 km

and

when motorist travel with  uniform velocity

than total time = 42 s

so velocity of motorist will be

velocity of motorist = \frac{S}{t}

velocity of motorist =  \frac{500}{42}  

velocity of motorist = 42.857 km/h

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3 years ago
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The heat transferred to and the work produced by the steam during this process  is 13781.618 kJ/kg

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W = 450 KJ

From the First Law of Thermodynamics, Q = U + W

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6 0
1 year ago
A cylindrical brass rod has a length of 5.00cm extending from a holder and a diameter of 4.50mm. Its Young's modulus is 98.0GPa.
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Answer:

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Explanation:

given data

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diameter = 4.50 mm

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load = 610 N

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what will be the elongation of the brass rod in mm

solution

we know here change in length formula that is express as

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δ = \frac{PL}{AE}  

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δ = 0.01956 mm

so elongation of the brass rod is 0.01956 mm

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