Answer:
2.35 yards/second or 7.07 ft/second
Step-by-step explanation:
The distance to be covered is 55 yards.
The casting cools at the rate of [tex]0.3^\circ \text F[/tex] and the temperature must not be allowed to cool more than [tex]7^\circ \text F[/tex].
We know that, [tex]\text {distance} = \frac{\text {speed}}{\text {time}}[/tex]
By the time, the temperature reaches [tex]7^\circ \text F[/tex], it will take about,
[tex]\frac{7}{0.3}=23.33\text s[/tex], so it will take about 23.33 seconds.
Also, 55 yards = [tex]55 \times 3 =165 ft[/tex]
So the minimum speed that conveyor must move is,
[tex]\frac{165}{23.33}=7.07 ft/s[/tex]
Hence, the speed of conveyor is 7.07 feet per second.
The minimum speed that the conveyor must move is about 7 ¹/₄ feet/second
Acceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem!
The castings cool at the rate of 0.3 °F per second and must not be allowed to cool more than 7°F before being heat treated.
[tex]\texttt{Maximum Time Allowed} = 7 \div 0.3 = \frac{70}{3} \texttt{ seconds}[/tex]
The minimum speed that the conveyor must move:
[tex]\texttt{Minimum Speed} = \texttt{Distance} \div \texttt{Maximum Time Allowed}[/tex]
[tex]\texttt{Minimum Speed} = 55 \div \frac{70}{3}[/tex]
[tex]\texttt{Minimum Speed} = 2\frac{5}{14} \texttt{ yards/second}[/tex]
[tex]\texttt{Minimum Speed} = 2\frac{5}{14} \times 3 \texttt{ feet/second}[/tex]
[tex]\texttt{Minimum Speed} = 7\frac{1}{14} \texttt{ feet/second}[/tex]
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Conveyor , Speed
