traveling with an initial speed of 70km/h. a car accelerates at 6000km/hr^2 along a straight road. how long will it take to reach a speed of 120km/hr? also, through what distance does the car travel during this time.?
v = v(o) +at,
a = (v-v(o))/a =(120-70)/6000 = 8.33•10^-3 h = 30 s.
s =v(o) •t+at^2/2 = 70•8.33•10^-3 + 6000•(8.33•10^-3)^2/2 = 0.79 km
To find out how long it will take for the car to reach a speed of 120 km/hr, we need to calculate the acceleration time.
Given:
Initial speed (u) = 70 km/hr
Final speed (v) = 120 km/hr
Acceleration (a) = 6000 km/hr^2
Step 1: Convert the speeds from km/hr to m/s.
u = 70 km/hr * (1 km/1000 m) * (1 hr/3600 s) = 19.44 m/s
v = 120 km/hr * (1 km/1000 m) * (1 hr/3600 s) = 33.33 m/s
Step 2: Use the formula of acceleration to find the time.
a = (v - u) / t
Rearranging the formula, we have:
t = (v - u) / a
t = (33.33 m/s - 19.44 m/s) / 6000 km/hr^2 * (1 km/1000 m) * (1 hr/3600 s) = 0.00054375 hrs
Step 3: Convert the time from hours to seconds.
t = 0.00054375 hrs * 3600 s/hr = 1.9575 s ≈ 1.96 s
So, it will take approximately 1.96 seconds for the car to reach a speed of 120 km/hr.
To calculate the distance the car travels during this time, we can use the formula:
Distance (s) = u * t + 0.5 * a * t^2
s = 19.44 m/s * 1.96 s + 0.5 * 6000 km/hr^2 * (1 km/1000 m) * (1 hr/3600 s) * (1.96 s)^2 = 38.09 m
Therefore, the car will travel approximately 38.09 meters during this time.
To find out how long it will take for the car to reach a speed of 120 km/hr and the distance it travels during this time, we need to use the equation of motion:
v = u + at
Where:
v = final velocity (120 km/hr)
u = initial velocity (70 km/hr)
a = acceleration (6000 km/hr^2)
t = time
First, let's convert the velocities from km/hr to m/s to be consistent with the standard SI units:
120 km/hr * (1/3.6) m/s = 33.33 m/s
70 km/hr * (1/3.6) m/s = 19.44 m/s
Now, let's calculate the time it takes for the car to reach a speed of 120 km/hr:
33.33 m/s = 19.44 m/s + a * t
Substituting the values:
33.33 m/s = 19.44 m/s + (6000 km/hr^2) * t
Since km/hr is not consistent with the SI units used here, we need to convert the acceleration as well:
6000 km/hr^2 * (1/3.6) m/s^2 = 1666.67 m/s^2
So, the equation becomes:
33.33 m/s = 19.44 m/s + 1666.67 m/s^2 * t
Now, let's solve for 't':
t = (33.33 m/s - 19.44 m/s) / 1666.67 m/s^2
t ≈ 0.0083 seconds (rounded to four decimal places)
Therefore, it will take approximately 0.0083 seconds for the car to reach a speed of 120 km/hr.
To find the distance traveled during this time, we can use the kinematic equation:
s = ut + (1/2)at^2
Where:
s = distance
u = initial velocity (19.44 m/s)
t = time (0.0083 s)
a = acceleration (1666.67 m/s^2)
Substituting the values:
s = (19.44 m/s * 0.0083 s) + (1/2) * (1666.67 m/s^2) * (0.0083 s)^2
Simplifying the equation:
s ≈ 0.161 meters (rounded to three decimal places)
Therefore, the car will travel approximately 0.161 meters during this time.