Ask question

Ask question

All categories

2 years ago

15

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t)=

bt2−ct3, where b = 3.00 m/s^2 and c = 0.100 m/s^3.
Required:
a. Calculate the average velocity of the car for the time interval t = 0 to t = 8.0 s.
b. Calculate the instantaneous velocity of the car at the following times:

1. t = 0
2. t = 4.0 s
3. t = 8.0 s

c. How long after starting from rest is the car again at rest?

1 answer:

True [87]2 years ago

6 0

Answer:

(a) average velocity = 17.6 m/s

(b) when t = 0, v = 0

when t = 4, v = 19.2 m/s

when t = 8, v = 28.8 m/s

(c) after starting from rest, the car will be at rest again in 20 s

Explanation:

Given;

x(t)=bt²−ct³, substitute the given values and the equation will become;

x(t)=3t²−0.1t³

(a)average velocity = total distance / total time

total distance, x(t) = 3t²−0.1t³

x(8) = 3t²−0.1t³

X(8) = 3(8)² - 0.1(8)³

X(8) = 140.8 m

total time = 8 s

average velocity = 140.8 / 8

average velocity = 17.6 m/s

(b) instantaneous velocity = dx / dt

dx / dt = 6t - 0.3t²

when t = 0

v = 0

when t = 4 s

v = 6(4) - 0.3(4²) = 19.2 m/s

when t = 8 s

v = 6(8) - 0.3(8²) = 28.8 m/s

(c) the velocity is zero at dx / dt = 0

6t - 0.3t² = 0

t(6 - 0.3t) = 0

t = 0 or 6 - 0.3t = 0

t = 0 or 0.3t = 6

t = 0 or t = 6 / 0.3

t= 0 or t = 20 s

After starting from rest, the car will be at rest again in 20 s

You might be interested in

A figure skater skates across a rink of length 50 m in 12.1 seconds. a. What is the average speed of the skater? (2 points) b. I

melamori03 [73]

(a) The skater covers a distance of S=50 m in a time of t=12.1 s, so its average speed is the ratio between the distance covered and the time taken:
$v= \frac{S}{t}= \frac{50 m}{12.1 s}=4.13 m/s$

(b) The initial speed of the skater is
$v_i = 4 m/s$
while the final speed is
$v_f = 5.3 m/s$
and the time taken to accelerate to this velocity is t=2 s, so the acceleration of the skater is given by
$a= \frac{v_f - v_i}{t}= \frac{5.3 m/s-4.0 m/s}{2.0 s}=0.65 m/s^2$

(c) The initial speed of the skater is
$v_i = 13.0 m/s$
while the final speed is
$v_f=0$
since she comes to a stop. The distance covered is S=8 m, so we can use the following relationship to find the acceleration of the skater:
$2aS=v_f^2 -v_i^2$
from which we find
$a= \frac{-v_i^2}{2S}= \frac{-(13.0m/s)^2}{2 \cdot 8.0 m}=-10.6 m/s^2$
where the negative sign means it is a deceleration.

4 0

2 years ago

A computer is connected across a 110 V power supply. The computer dissipates 123 W of power in the form of electromagnetic radia

nexus9112 [7]

Answer:

81.3ohms

Explanation:

Resistance is known to provide opposition to the flow of electric current in an electric circuit.

Power dissipated by the computer is expressed as;

Power = current (I) × Voltage(V)

P = IV... (1)

Note that from ohms law, V = IR

I = V/R ... (2)

Substituting equation 2 into 1, we will have;

P = (V/R)×V

P = V²/R.. (3)

Given source voltage = 100V, Power dissipated = 123W

To get resistance R of the computer, we will substitute the given value into equation 3 to have

123 = 100²/R

R = 100²/123

R = 10,000/123

R = 81.3ohms

The resistance of the computer is 81.3ohms

3 0

2 years ago

Read 2 more answers

If a 100-N net force acts on a 50-kg car, what will the acceleration of the car be?

Tema [17]

Newton's 2nd law of motion:

   Force = (mass) x (acceleration)

Divide each side by (mass):

   Acceleration = (force) / (mass)

   = (100 N) / (50 kg)

   = 2 m/s²

5 0

2 years ago

# 5 what will most likely happen when an air mas of low temperature exists above a water body at a higher temperature?

laila [671]

Answer: Heat will transfer from the water to the air. When a mass of air moves on a warmer surface it is heated by its base. Then thermal instability develops in the lower layers and then extends upwards. If the air initially contained inversions, these are destroyed and a strong gradient is established uniformly in the lower troposphere temperature.

3 0

1 year ago

Read 2 more answers

I need help with this

lisabon 2012 [21]

A. Condensation

Hope this helps!!!

5 0

1 year ago